Domain Walls and Phase Transitions in the Frustrated Two-Dimensional XY Model

TL;DR

This paper investigates the critical properties of the 2D XY model with magnetic filling factors 1/3 and 2/5, focusing on domain walls and phase transitions, and finds universality with the 2D Ising model.

Contribution

It compares domain wall structures and phase transitions in the 2D XY model at different fillings, including effects of disorder, revealing universality classes.

Findings

First order phase transition at f=2/5 due to domain wall binding.

Second order transition at f=1/3 with linear critical interface.

Disorder causes f=2/5 transition to fall into the 2D Ising universality class.

Abstract

We study and compare the critical properties of the two-dimensional (2D) XY model in a transverse magnetic field with magnetic filling factors f=1/3 and f=2/5. In addition to the spin waves, the low energy excitations of the system consist of various domain walls between degenerate ground states. The lowest energy domain wall has a similar structure for both f=1/3 and f=2/5 and its properties dictate the nature of the phase transition. For f=2/5 these lowest energy walls have a negative energy for binding to each other, giving rise to a branching domain-wall structure and leading to a first order phase transition. For f=1/3 this binding energy is positive, resulting in a linear critical interface. In order to make a comparison to recent experiments, we investigate the effect of small quenched bond disorder for f=2/5. A finite-size scaling analysis of extensive Monte Carlo simulations strongly suggests that the critical exponents of the phase transition for f=1/3, and for f=2/5 with disorder, fall into the universality class of the two-dimensional Ising model.